That's not possible. The IFF is only in effect if the ball is fair. The call actually is "infield fly if fair." If it's foul, the rule doesn't apply. So when do you declare a dead ball? A foul ball caught is a live play with 0 or 1 outs.
Otherwise, I see your point but disagree. The IFR is designed to avoid the intentional drop double play but nothing more. In all other respects, it treats the play exactly as it would be but for the one specific thing it's trying to protect.
Imagine: Amazing nearly unhittable closer comes into the game. Bases loaded, one out, walk off situation. Ricky Henderson style speed on third. Third base coach says we're tagging on any pop up. It's our best chance. If it's farther than 100 feet from home plate, you're going. If the catcher has to turn around to catch it in foul territory, you're going. A foul ball near the dugouts, you're going. Infielders at DP depth. Pop up about 20 feet behind first base. If you call it a dead ball, the runner on third cannot advance on a caught ball. Why should that option be taken away?